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Abstract
Imagine that you receive information on the choices made by a decision maker (DM) from all subsets of some set X. You know nothing about the context of these choices. You look for an explanation for the DM’s behavior. You would probably look first for a single rationale explaining the behavior. Specifically, you would seek a rationalizing ordering—that is, a linear ordering on X, such that for every choice set A ⊆ X, the DM’s choice from A is the best element in A according to the ordering. You recall that the “Independence of Irrelevant Alternatives” Axiom (IIA)—which requires that the chosen element from a set also be chosen from every subset that contains it—is a necessary and sufficient condition for the existence of such an explanation.
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